If A is a matrix of order m × n and B is a matrix such that A B ' and B ' A are both defined, then the order of matrix B is:

Question

If $A$ is a matrix of order $m \times n$ and $B$ is a matrix such that $A B'$ and $B' A$ are both defined, then the order of matrix $B$ is:

Smart Achievers · Accepted Answer

(4)

Ans. $m \times n$

Explanation:

Let $A = {[a_{i j}]}_{m \times n}$
and $B = {[b_{i j}]}_{p \times q}$

$∴$ $B' = {[b_{i j}]}_{q \times p}$

Now, $A B'$ is defined, so $n = q$

and $B' A$ is also defined, so $p = m$

$∴$ $Order of B is m \times n$

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